An important case is the potential \(\psi = \frac{\left\Vert \cdot  \right\Vert ^2}{2}\) , where \(\left\Vert \cdot  \right\Vert \)  denotes the Euclidean norm.
Then, the Bregman divergence becomes \(D_\psi (x,y) = \frac{1}{2}\left\Vert x-y \right\Vert ^2\) .
For more background on Bregman divergence and its properties, see, e.g., [1]} and [2]}.
